A wireless mesh network is a multi-hop network consisting nodes called mesh routers and mesh clients. In the network, communication between a pair of nodes happens when both nodes share a same channel. Channel assignment is an application in graph theory on the vertex coloring. The channels are allocated in such a way to minimize the bandwidth with the constraints of avoiding the electromagnetic interference. In this paper, we focus on the channel allocation for multi-channel which considers adjacent-channel constraint, cochannel and cosite constraint. The minimum number of the channels that are used in the network with minimum completion time shows the effectiveness of the work.